Convergence, stability, and discrete approximation of laplace spectra

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2010, Pages 650-663

  Dey, Tamal K ^a   Ranjan, Pawas ^a   Wang, Yusu ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MESH GENERATION; SPECTROSCOPY;

CONVERGENCE RESULTS; DISCRETE APPROXIMATION; DISCRETE LAPLACE OPERATORS; GEOMETRIC OPTIMIZATION; LAPLACE-BELTRAMI OPERATOR; LAPLACIAN SPECTRA; SHAPE SEGMENTATION; SPECTRAL STRUCTURE;

LAPLACE TRANSFORMS;

EID: 77951694243     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973075.54     Document Type: Conference Paper

References (24)

1. M. Belkin and P. Niyogi. Laplacian Eigenmaps for dimensionality reduction and data representation. Neural Computation, 15(6):1373-1396, 2003.
2. M. Belkin and P. Niyogi. Convergence of Laplacian Eigenmaps. Preprint, 2008.
3. M. Belkin, J. Sun, and Y. Wang. Discrete Laplace operator on meshed surfaces. In Proc. 24st Annu. ACM Sympos. Comput. Geom., pages 278-287, New York, NY, USA, 2008. ACM.
4. M. Desbrun, M. Meyer, P. Schröder, and A. H. Barr. Implicit fairing of irregular meshes using diffusion and curvature flow. Computer Graphics, 33(Annual Conference Series):317-324, 1999.
5. J. Dodziuk. Finite-difference approach to the hodge theory of harmonic forms. American Journal of Mathematics, 98(1):79-104, 1978.
6. K. Hildebrandt, K. Polthier, and M. Wardetzky. On the convergence of metric and geometric properties of polyhedral surfaces. Geometriae Dedicata, 123(1):89-112, December 2006.
7. T. Kato. Perturbation Theory for Linear Operators. Springer-Verlag New York Inc., 1966.
8. B. Levy. Laplace-beltrami eigenfunctions: Towards an algorithm that understands geometry. In IEEE International Conference on Shape Modeling and Applications, invited talk, 2006.
9. d via diffusion metric. Computer Graphics Forum, 28(5):1497-1508, 2009.
10. C. Luo, J. Sun, and Y. Wang. Integral estimation from point cloud in d-dimensional space: A geometric view. In Proc. 25st Annu. ACM Sympos. Comput. Geom., 2009, To appear.
11. U. F. Mayer. Numerical solutions for the surface diffusion flow in three space dimensions. comput. Appl. Math, 20(3):361-379, 2001.
12. M. Meyer, M. Desbrun, P. Schröder, and A. H. Barr. Discrete differential geometry operators for triangulated 2-manifolds. In Proc. VisMath'02, Berlin, Germany, 2002.
13. U. Pinkall and K. Polthier. Computing discrete minimal surfaces and their conjugates. Experimental Mathematics, 2(1):15-36, 1993.
14. M. Reuter, F.-E. Wolter, and N. Peinecke. Laplace-beltrami spectra as "shape-dna" of surfaces and solids. Computer-Aided Design, 38(4):342-366, 2006.
15. O. Sorkine. Differential representations for mesh processing. Computer Graphics Forum, 25(4):789-807, 2006.
16. M. E. Taylor. Partial Differential Equations: Basic Theory. Springer-Verlag New York Inc., 1996.
17. K. Thangudu. Practicality of laplace operator, 2009. Master Thesis, The Ohio State University, Computer Science and Engineering Department.
18. U. von Luxburg, M. Belkin, and O. Bousquet. Consistency of spectral clustering. Ann. Statist., 36(2):555-586, 2008.
19. M. Wardetzky. Discrete Differential Operators on Polyhedral Surfaces - Convergence and Approximation. PhD thesis, Freie Universität Berlin, 2006.
20. M. Wardetzky. Convergence of the cotangent formula: An overview. In A. I. Bobenko, J. M. Sullivan, P. Schröder, and G. Ziegler, editors, Discrete Differential Geometry, pages 89-112. Birkhuser, to appear.
21. M. Wardetzky, S. Mathur, F. Kälberer, and E. Grinspun. Discrete laplace operators: no free lunch. In Proc. 5th Sympos. Geom. Processing, pages 33-37, 2007.
22. G. Xu. Discrete laplace-beltrami operators and their convergence. Comput. Aided Geom. Des., 21(8):767-784, 2004.
23. Z. Xu, G. Xu, and J.-G. Sun. Convergence analysis of discrete differential geometry operators over surfaces. In IMA Conference on the Mathematics of Surfaces, pages 448-457, 2005.
24. H. Zhang, O. van Kaick, and R. Dyer. Spectral mesh processing. Computer Graphics Forum, accepted, 2009.